Collimator lens and optical scanning device which uses it

ABSTRACT

A collimator lens having only two lens elements, wherein the surface of the collimator lens nearest the collimated light side is concave, and at least one of the two lens elements includes an aspherical surface having diffraction optical element zones thereon which provide dispersion of opposite sign to the dispersion provided by refraction of light by the lens element on which said zones are formed. Preferably, a specified condition is satisfied in order to facilitate manufacture of diffraction zones of the diffraction optical element (DOE) surface(s).

BACKGROUND OF THE INVENTION

Various optical scanning devices used in laser beam scanning such as incopy machines, laser printers, and the like, or for recording ordisplaying picture images are conventionally known. Such opticalscanning devices generally use a collimator lens to collimate the lightbeam received from, for example, a semiconductor laser, and areconstructed so as to scan an image using a rotating multi-faceted mirrorand an f·θ lens. Collimator lenses consisting of two lens elements aredisclosed in Japanese Laid Open Patent Applications S58-14109,S58-38915, S61-279820, S61-273520, and H2-73324. These collimator lensesare light in weight and compact.

When using a collimator lens in conjunction with an optical scanningdevice, the numerical aperture of the collimator lens that is employedis generally larger than that of the f 0 lens, in order to obtain highefficiency in gathering the light from a light source. However, such adesign produces greater aberrations. Therefore, the aberrations of thecollimator lens generally need to be corrected carefully.

Furthermore, in an optical scanning device, a multiple beam format isused for multi-beam scanning that uses multiple light sources, making itpossible to either increase the scan speed or to make simultaneousrecordings in one scan. In cases where a multi-beam format is used,favorable aberration correction is desirable within a half-picture angleso of two degrees.

With the above-mentioned collimator lenses, little consideration hasapparently been given to the performance of the collimator lens at largepicture angles. If the picture angle is large, since the variousaberrations become troublesome, it becomes difficult to successfully usethese lenses in a multibeam scanning optical system in which multiplelight sources are arranged on a plane surface that is normal to theoptical axis. In addition, in the case where use is made of asemiconductor laser as the light source, the phenomenon of mode hoppingoccurs as a result of changes in the ambient temperature or changes inthe drive current. When mode hopping occurs, the output wavelength ofthe laser shifts, and this results in the position of the focus on theimage-forming surface shifting due to the system magnification beingdependent on the wavelength of the light. Thus, mode hopping makes itmore difficult to record information with a high degree of resolution inthat the various aberrations need to be well-corrected relative to theoscillation wavelength of the laser. However, the prior art collimatorlenses referred to above do not adequately correct for aberrations dueto a change in oscillation wavelength of the light source.

BRIEF SUMMARY OF THE INVENTION

The present invention relates to a collimator lens used in scanningdevices, such as copy machines, laser printers and the like, forscanning laser beams, and recording or displaying an image. Inparticular, it relates to a collimator lens, and the optical scanningdevice which uses it, for converting optical flux emitted by asemiconductor laser into a collimated beam. A first object of thepresent invention is to provide a collimator lens that can be used toscan multiple light sources wherein off-axis aberrations are favorablycorrected for a half-picture angle of 2 degrees. A second object of theinvention is to provide a collimator lens which favorably corrects foraberrations due to a change in oscillation wavelength of the lightsource.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will become more fully understood from thedetailed description given below and the accompanying drawings, whichare given by way of illustration only and thus are not limitative of thepresent invention, wherein:

FIG. 1 shows the basic lens element structure of a collimator lensrelating to Embodiment 1;

FIG. 2 shows the basic lens element structure of a collimator lensrelating to Embodiment 2;

FIG. 3 illustrates an optical scanning device which uses the collimatorlens shown in FIG. 1;

FIGS. 4A-4F show the spherical aberration, astigmatism, distortion,lateral color, the phase difference function Φ(y), and the slope ofΦ(y), respectively, of the collimator lens of Embodiment 1;

FIGS. 5A-5F show the spherical aberration, astigmatism, distortion,lateral color, the phase difference function Φ(y), and the slope ofΦ(y), respectively, of the collimator lens of Embodiment; 2;

FIGS. 6A-6D show the spherical aberration, astigmatism, distortion, andlateral color, respectively, of the collimator lens of Embodiment 3;

FIGS. 6E & 6F show the phase difference function Φ(y), and the slope ofΦ(y) of surface #1 of the collimator lens of Embodiment 3;

FIGS. 6G & 6H show the phase difference function Φ(y), and the slope ofΦ(y) of surface #2 of the collimator lens of Embodiment 3;

FIG. 7A-7F show the spherical aberration, astigmatism, distortion,lateral color, phase difference function Φ(y), and slope of Φ(y),respectively, of the collimator lens of Embodiment 4;

FIGS. 8A-8F show the spherical aberration, astigmatism, distortion,lateral color, phase difference function Φ(y), and slope of Φ(y),respectively, of the collimator lens of Embodiment 5;

FIGS. 9A-9D show the spherical aberration, astigmatism, distortion, andlateral color, respectively, of the collimator lens of Embodiment 6;

FIGS. 9E & 9F show the phase difference function Φ(y), and the slope ofΦ(y) of surface #3 of the collimator lens of Embodiment 6;

FIGS. 9G & 9H show the phase difference function Φ(y), and the slope ofΦ(y) of surface #4 of the collimator lens of Embodiment 6;

FIGS. 10A-10F show the spherical aberration, astigmatism, distortion,lateral color, phase difference function Φ(y), and slope of Φ(y),respectively, of the collimator lens of Embodiment 7;

FIGS. 11A-11D show the spherical aberration, astigmatism, distortion,and lateral color, respectively, of the collimator lens of Embodiment 8;

FIGS. 11E & 11F show the phase difference function Φ(y), and the slopeof Φ(y) of surface #3 of the collimator lens of Embodiment 8; and,

FIGS. 11G & 11H show the phase difference function Φ(y), and the slopeof Φ(y) of surface #4 of the collimator lens of Embodiment 8.

DETAILED DESCRIPTION

The present invention is a collimator lens that employs a simple,two-lens-element construction, wherein the two lens elements are fixedin position relative to each other and aberrations which occur withmulti-beam scanning are favorably corrected for a half-picture angle ωof up to 2 degrees. Furthermore, it is an objective of the invention toprovide a collimator lens and a scanning device which uses it that alsoprovide correction relative to changes in the oscillation wavelength ofthe light source.

The collimator lens of the present invention is characterized by thefact that it is constructed of only two lens elements, wherein at leastone surface thereof is a diffraction optical element (hereinafter DOE)that includes diffractive zones on an aspheric surface. In addition, theinvention is characterized by the fact that the lens element surface atthe collimated light side of the collimator lens is concave.

Furthermore, the collimator lens may be constructed in two ways, asfollows, in order from the collimated light side: a first lens elementhaving negative refractive power and a second lens element havingpositive refractive power, or a first lens element which has positiverefractive power and a second lens element which has positive refractivepower. In the case of the latter, it is desirable that the refractivepower of the first lens element be established to be larger than therefractive power of the second lens element.

In addition, it is desirable that the following Condition (1) besatisfied:

|dΦ(y)/dy|<300  Condition (1)

where,

|dΦ(y)/dy| is the absolute value of the slope of the function Φ(y), withΦ(y) being the phase difference function of the DOE optical surface, andy being the distance from the optical axis.

Furthermore, the optical scanning device of the present invention ischaracterized by the fact that it employs the collimator lens of thepresent invention.

A characteristic of a DOE surface is that the dispersion thereof islarger and of an opposite sign to that of ordinary glass, as shownbelow.

Ordinary glass relative dispersion:

1/ν=(N₁−N₃)/(N₂−1)

where

N₁, N₂, and N₃ are the refractive index relative to wavelengths λ₁, λ₂,and λ₃, respectively, with λ₁<λ₂<λ₃.

DOE surface relative dispersion:

1/ν=(λ₁−λ₃)/λ₂.

When mode hopping of a semiconductor laser at a standard wavelength of780 nm is considered, with a wavelength change of ±20 nm, the reciprocalrelative dispersion ν (i.e., the Abbe number) equals 611 for ordinaryglass (BK-7) and equals −19.5 for the DOE surface, thus the relativedispersion 1/ν of the DOE is much larger and of the opposite sign ascompared to that of glass. Therefore, by using a DOE surface, a lenshaving only a few lens elements can provide a reduced movement of thefocal position due to mode hopping.

The DOE phase difference function is given by:

Φ(y)=b₁y²+b₂y⁴+b₃y⁶  Equation (1)

where

Φ(y) is the phase difference function of the DOE surface,

y is the distance from the optical axis, and

b₁, b₂, and b₃ are coefficients.

The aspherical DOE surface profile is given by:

Z=(Φ(y)±2nπ)·(λ/(2T(N−1)))+(y²/r)/(1+(1−ky²/r²)^(½))+a₄y⁴+a₆y⁶+a₈y⁸+a₁₀y¹⁰  Equation(2)

where

Z is the distance of the DOE surface from a plane tangent to the DOEsurface vertex at a distance y from the optical axis,

n is the DOE ring number (n=0, 1, 2 . . . ),

N is the refractive index at the standard wavelength,

k is an eccentricity factor, and

a₄, a₆, a₈, and a₁₀ are aspherical surface coefficients of the surfaceprofile.

The number of zones of the DOE surface, and the pitch of each zone isdetermined by the phase difference function, and relative to the heighty from the optical axis, to the extent that changes of the phasedifference function become larger, then the pitch of each zone becomessmaller, and the unevenness of the DOE surface becomes greater.

If the pitch of each zone is small, and the unevenness is great, thenprocessing becomes difficult. Hence, if the correct unevenness of thesurface profile is not formed, the performance will completely breakdown. Therefore, it is desirable that Condition (1) above be satisfied.

In the case where the collimator is formed of two convex lens elements,there is a tendency for the first lens element to have strong refractivepower. In such a case, as well as the case where the collimator lens isformed of the combination of a concave lens element and a convex lenselement, the height of the optical rays which are incident onto the lenssurface which has the stronger refractive power can be increased, bywhich means (since the Petzval sum can be made smaller), the curvatureof the image surface can be corrected. On the other hand, whenconstruction is accomplished with two convex lens elements, sphericalaberration can be corrected by making the first lens element have astrong refractive power.

A generalized description of the collimator lens of the invention willnow be given with reference to the drawings.

FIG. 1 shows the basic lens element construction of the collimator lensof Embodiments 1 and 4 of the present invention. FIG. 2 shows the basiclens element construction of the collimator lens of Embodiments 2, 3 and5-8. FIG. 3 shows the basic components of an optical scanning devicewhich uses the collimator lens of Embodiments 1-8.

The optical scanning device 2, as shown in FIG. 3, converts a laser beamemitted from the semiconductor laser 3 into collimated light by means ofthe collimator lens 1. A compensation optical system 4, formed using aslit, cylindrical lens, or the like, corrects deficiencies of thepolygon mirror 5. The laser beam is deflected by means of the rotatingpolygon mirror 5, and a minute spot of light is guided to the surface ofthe light-conducting, photo-sensitive drum 7 by means of f·θ lens 6.Thus, the drum 7 is scanned by the scanning beam as the drum is rotated.

As shown in FIGS. 1 and 2, the collimator lens 1 of the presentinvention is formed by arranging, in order from the collimated lightside of the collimator lens: a first lens element L₁ which has positiveor negative refractive power, and has a concave surface on thecollimated light side, and a second lens element L₂ which has positiverefractive power and a convex surface on the side of the semiconductorlaser 3. In addition, at least one lens element surface is a DOEsurface.

In FIGS. 1 and 2, the optical axis is labeled X.

Furthermore, the shape of the aspherical, DOE surface(s) is (are) givenby Equations (1) and (2) above, and the collimator lens satisfies theabove Condition (1).

By satisfying Condition (1), the pitch of each diffraction zone of theDOE surface(s) can be made larger and, since the height of theunevenness of the optical surface does not become larger to the sameextent, the process of manufacturing the DOE surface(s) becomes easier.Thus, the formation of the desired surface profile with high precisionis easier to accomplish.

With a collimator lens 1 constructed in the manner described above,although the collimator lens consists of only two lens elements, thenumerical aperture can be as large as approximately 0.25-0.3 whileproviding a collimator lens having its off-axis aberrations favorablycorrected, as is desirable in an optical scanning device which employsmultiple scanning beams.

The collimator lens 1 of the present invention also enables the opticalflux on the optical source side to be nearly telecentric. Thus, even ifthe light source is not positioned accurately on the optical axis, thelens performance will not deteriorate.

Using this characteristic, the collimator lens 1 of the presentinvention can be used in a multi-beam scanning optical system whereinmultiple semiconductor lasers are arranged in a line that is normal tothe optical axis. For example, in a color copier device, threesemiconductor lasers can be arranged corresponding to the colors red,green, and blue, respectively. Also, dual monochrome and color use canbe provided by arranging four semiconductor lasers in a line that isnormal to the optical axis. In addition, by arranging multiplesemiconductor lasers for monochrome use in the direction of duplicatescanning, the number of scans can be reduced, thereby compressing theoptical scanning time.

The collimator lens 1 of the present invention can be used to form animage of an object onto a recording medium, as well as to collect thelight of a laser beam at an image surface. Thus the collimator lens ofthe present invention can be used as a lens for scanning or as a lensfor an optical pickup, such as with an optical disk. In the case wherethe collimator lens 1 of the present invention is used in the mannerindicated above, the focal distance of the entire lens system isdesirably within the range of 3-30 mm.

A detailed description of Embodiments 1-8 will now be given, usingspecific numerical values.

EMBODIMENT 1

As shown in FIG. 1, the collimator lens 1 relating to Embodiment 1 isconstructed, in order from the collimated light side, of a first lenselement L₁ having a positive meniscus shape with its concave surface onthe collimated light side, and a second lens element L₂ having apositive meniscus shape. Further, the collimated light side of the firstlens element L₁ is made to be a DOE surface having an asphericalsubstrate.

Table 1 below lists the surface number #, in order from the collimatedlight side of the collimator lens, the radius of curvature R (in mm) ofeach lens element surface, the spacing D (in mm) between the surfaces,as well as the refractive index N at the wavelengths 760 nm, 780 nm and800 nm. The surface with a * to the right of the surface number is anaspheric, DOE surface. In the middle portion of the table, are listedthe numerical aperture NA, the focal length f′ of the collimator lens,the focal length f₁ of the first lens element in order from thecollimated light side, the focal length f₂ of the second lens element inorder from the collimated light side, and the radius of curvature r₁ ofa spherical surface having the same vertex point and two endpoints of aneffective diameter as that of the concave, aspherical surface nearestthe collimated light side. In the lower portion of the table are listedthe values of k, a₄, a₆, a₈, and a₁₀, as well as the values of thecoefficients b₁, b₂, and b₃ for Equations (1) and (2) above relating tosurface #1.

TABLE 1 # R D N<760 nm> N<780 nm> N<800 nm> 1* −34.147 4.167 1.583021.58252 1.58205 2 −6.485 0.854 3 −15.156 4.070 1.49314 1.49283 1.49253 4−7.811 NA = 0.25 f′ = 10 f₁ = 12.66 f₂ = 27.65 r₁ = −20.18 Asphericaland DOE coefficients of surface #1: k  =  9.4285 b₁ = −1.1587 × 10 a₄  =−1.4311 × 10⁻³ b₂ = −1.7891 × 10⁻² a₆  = −2.1656 × 10⁻⁵ b₃ = −8.1526 ×10⁻⁶ a₈  = −9.5676 × 10⁻⁷ a₁₀ =  6.8918 × 10⁻⁹

FIGS. 4A-4F show the spherical aberration, astigmatism, distortion,lateral color, the 15 phase difference function Φ(y), and the slope ofΦ(y), respectively, of the collimator lens of Embodiment 1.

EMBODIMENT 2

The collimator lens 1 of Embodiment 2 is formed, in order from thecollimated light side, of a first lens element L₁ having a negativemeniscus shape with its convex surface on the collimated light side, anda second lens element L₂ having a biconvex shape, wherein the surface onthe light source side of the first lens element L₁ is a DOE surface.

Table 2 below lists the surface number #, in order from the collimatedlight of the collimator lens, the radius of curvature R (in mm) of eachlens element surface, the spacing D (in mm) between the surfaces, aswell as the refractive index N at the wavelengths 760 nm, 780 nm and 800nm. The surface with a * to the right of the surface number is anaspheric, DOE surface. In the middle portion of the table, are listedthe numerical aperture NA, the focal length f′ of the collimator lens,the focal length f₁ of the first lens element in order from thecollimated light side, and the focal length f₂ of the second lenselement in order from the collimated light side. In the lower portion ofthe table are listed the values of k, a₄, a₆, a₈, and a₁₀, as well asthe values of the coefficients b₁, b₂, and b₃ for Equations (1) and (2)above relating to surface #2.

TABLE 2 # R D N<760 nm> N<780 nm> N<800 nm> 1 −7.023 2.564 1.583021.58252 1.58205 2* −17.769 0.500 3 25.148 4.167 1.77771 1.77690 1.776134 −8.546 NA = 0.25 f′ = 10 f₁ = −24.19 f₂ = 8.68 Aspherical and DOEcoefficients of surface #2: k  =  1.8485 b₁ = −1.5721 × 10 a₄  =  8.9347× 10⁻⁴ b₂ = −2.1988 × 10⁻¹ a₆  =  1.4092 × 10⁻⁵ b₃ = −7.2516 × 10⁻⁴ a₈ =  4.4457 × 10⁻⁷ a₁₀ = −1.2172 × 10⁻⁸

FIGS. 5A-5F show the spherical aberration, astigmatism, distortion,lateral color, the phase difference function Φ(y), and the slope ofΦ(y), respectively, of the collimator lens of Embodiment 2.

EMBODIMENT 3

The collimator lens 1 of Embodiment 3 has approximately the sameconstruction as Embodiment 2, however, both surfaces of the first lensL₁ are aspherical, DOE surfaces having phase difference functions andprofiles as defined by Equations (1) and (2) above.

Table 3 below lists the surface number #, in order from the collimatedlight side of the collimator lens, the radius of curvature R (in mm) ofeach lens element surface, the spacing D (in mm) between the surfaces,as well as the refractive index N at the wavelengths 760 nm, 780 nm and800 nm. The surfaces with a * to the right of the surface number areaspheric, DOE surfaces. In the middle portion of the table, are listedthe numerical aperture NA, the focal length f′ of the collimator lens,the focal length f₁ of the first lens element in order from thecollimated light side, the focal length f₂ of the second lens element inorder from the collimated light side, and the radius of curvature r₁ ofa spherical surface having the same vertex point and two endpoints of aneffective diameter as that of the concave, aspherical surface nearestthe collimated light side. In the lower portion of the table are listedthe values of k, a₄, a₆, a₈, and a₁₀, as well as the values of thecoefficients b₁, b₂, and b₃ for Equations (I) and (2) above relating tosurfaces #1 and 2.

TABLE 3 # R D N<760 nm> N<780 nm> N<800 nm> 1* −6.702 4.055 1.583021.58252 1.58205 2* −10.378 0.366 3 25.913 3.000 1.76279 1.76202 1.761294 −11.691 NA = 0.30 f′ = 10 f₁ = −69.10 f₂ = 10.95 r₁ = −6.33 Asphericaland DOE Aspherical and DOE coefficients of Surface #1: coefficients ofSurface #2: k  =  1.2020 k  =  6.7062 × 10⁻¹ a₄  = −5.8734 × 10⁻⁴ a₄  = 6.3675 × 10⁻⁵ a₆  =  1.2009 × 10⁻⁵ a₆  =  8.2780 × 10⁻⁶ a₈  = −1.5243 ×10⁻⁷ a₈  =  2.7643 × 10⁻⁸ a₁₀ =  2.8266 × 10⁻⁸ a₁₀ =  2.8441 × 10⁻⁹ b₁ = 2.1220 × 10 b₁ = −2.7117 × 10 b₂ =  1.2193 × 10⁻¹ b₂ = −6.1722 × 10⁻²b₃ = −5.3965 × 10⁻⁵ b₃ = −7.3727 × 10⁻⁴

FIGS. 6A-6D show the spherical aberration, astigmatism, distortion, andlateral color, respectively, of the collimator lens of Embodiment 3.FIGS. 6E & 6F show the phase difference function Φ(y) and the slope ofΦ(y), respectively, of surface #1 of this embodiment, and FIGS. 6G & 6Hshow the phase difference function Φ(y) and the slope of Φ(y),respectively, of surface #2 of this embodiment.

EMBODIMENT 4

The collimator lens 1 of Embodiment 4 has the same basic lens elementconfiguration as that of Embodiment 1.

Table 4 below lists the surface number #, in order from the collimatedlight side of the collimator lens, the radius of curvature R (in mm) ofeach lens element surface, the spacing D (in mm) between the surfaces,as well as the refractive index N at the wavelengths 760 nm, 780 nm and800 nm. The surface with a * to the right of the surface number is anaspheric, DOE surface. In the middle portion of the table, are listedthe numerical aperture NA, the focal length f′ of the collimator lens,the focal length f₁ of the first lens element in order from thecollimated light side, the focal length f₂ of the second lens element inorder from the collimated light side, and the radius of curvature r₁ ofa spherical surface having the same vertex point and two endpoints of aneffective diameter as that of the concave, aspherical surface nearestthe collimated light side. In the lower portion of the table are listedthe values of k, a₄, a₆, a₈, and a₁₀ as well as the values of thecoefficients b₁, b₂, and b₃ for Equations (1) and (2) above relating tosurface #1.

TABLE 4 # R D N<760 nm> N<780 nm> N<800 nm> 1* −39.615 5.000 1.583021.58252 1.58205 2 −7.735 0.904 3 −14.420 2.063 1.79175 1.79092 1.79013 4−8.697 NA = 0.25 f′ = 10 f₁ = 15.00 f₂ = 23.90 r₁ = −22.15 Asphericaland DOE Coefficients of Surface #1: k  =  1.0004 b₁ = −1.3561 × 10 a₄  =−1.3443 × 10⁻³ b₂ = −2.6709 × 10⁻¹ a₆  = −1.7907 × 10⁻⁵ b₃ = −2.7744 ×10⁻⁵ a₈  = −6.7866 × 10⁻⁷ a₁₀ = −2.7310 × 10⁻⁹

FIG. 7A-7F show the spherical aberration, astigmatism, distortion,lateral color, phase difference function Φ(y), and slope of Φ(y),respectively, of the collimator lens of Embodiment 4.

EMBODIMENT 5

The collimator lens 1 of Embodiment 5 has the same basic lens elementconfiguration as that of Embodiment 2, except that, in this embodiment,the surface on the collimated light side of the second lens element L₂isan aspherical, DOE surface.

Table 5 below lists the surface number #, in order from the collimatedlight side of the collimator lens, the radius of curvature R (in mm) ofeach lens element surface, the spacing D (in mm) between the surfaces,as well as the refractive index N at the wavelengths 760 nm, 780 nm and800 nm. The surface with a * to the right of the surface number is anaspheric, DOE surface. In the middle portion of the table, are listedthe numerical aperture NA, the focal length f′ of the collimator lens,the focal length f₁ of the first lens element in order from thecollimated light side, and the focal length f₂ of the second lenselement in order from the collimated light side. In the lower portion ofthe table are listed the values of k, a₄, a₆, a₈, and a₁₀, as well asthe values of the coefficients b₁, b₂, and b₃ for Equations (1) and (2)above relating to surfaces #3.

TABLE 5 # R D N<760 nm> N<780 nm> N<800 nm> 1 −4.546 2.636 1.791751.79092 1.79013 2 −6.201 0.732 3* 12.293 2.500 1.58302 1.58252 1.58205 4−13.666 NA = 0.25 f′ = 10 f₁ = −72.61 f₂ = 11.17 Aspherical and DOEcoefficients of surface #3: k  =  9.8034 × 10⁻¹ b₁ = −1.1640 × 10 a₄  =−2.6109 × 10⁻⁴ b₂ = −2.8818 × 10⁻² a₆  = −8.1066 × 10⁻⁷ b₃ =  4.5261 ×10⁻⁷ a₈  = −4.6880 × 10⁻⁸ a₁₀ =  2.0499 × 10⁻⁹

FIGS. 8A-8F show the spherical aberration, astigmatism, distortion,lateral color, phase difference function Φ(y), and slope of Φ(y),respectively, of the collimator lens of Embodiment 5.

EMBODIMENT 6

The collimator lens 1 of Embodiment 6 is constructed approximately thesame as Embodiment 5, however, in Embodiment 6, both surfaces of thesecond lens element L₂ are aspherical DOE surfaces.

Table 6 below lists the surface number #, in order from the collimatedlight side of the collimator lens, the radius of curvature R (in mm) ofeach lens element surface, the spacing D (in mm) between the surfaces,as well as the refractive index N at the wavelengths 760 nm, 780 nm and800 nm. The surfaces with a * to the right of the surface number areaspheric, DOE surfaces. In the middle portion of the table, are listedthe numerical aperture NA, the focal length f′ of the collimator lens,the focal length f₁ of the first lens element in order from thecollimated light side, and the focal length f₂ of the second lenselement in order from the collimated light side. In the lower portion ofthe table are listed the values of k, a₄, a₆, a₈, and a₁₀, as well asthe values of the coefficients b₁, b₂, and b₃ for Equations (1) and (2)above relating to surfaces #3 and #4.

TABLE 6 # R D N<760 nm> N<780 nm> N<800 nm> 1 −5.487 4.533 1.791751.79092 1.79013 2 −7.805 1.833 3* 10.015 3.667 1.58302 1.58252 1.582054* −31.162 NA = 0.30 f′ = 10 f₁ = −171.30 f₂ = 12.97 Aspherical and DOEAspherical and DOE coefficients of surface #3: coefficients of Surface#4: k  =  1.0236 k  =  1.0021 a₄  = −7.2045 × 10⁻⁵ a₄  =  1.5307 × 10⁻⁴a₆  =  3.2211 × 10⁻⁸ a₆  =  1.5735 × 10⁻⁷ a₈  =  8.2613 × 10⁻⁹ a₈  = 7.3761 × 10⁻⁹ a₁₀ = −4.2583 × 10⁻¹⁰ a₁₀ = −6.2605 × 10⁻¹⁰ b₁ = −6.7453× 10 b₁ = −5.4124 × 10 b₂ = −5.7822 × 10⁻³ b₂ = −4.3078 × 10⁻³ b₃ =−1.4254 × 10⁻⁵ b₃ = −8.7963 × 10⁻⁶

FIGS. 9A-9D show the spherical aberration, astigmatism, distortion, andlateral color, respectively, of the collimator lens of Embodiment 6.FIGS. 9E & 9F show the phase difference function Φ(y) and the slope ofΦ(y), respectively, of surface #3 of this embodiment, and FIGS. 9G & 9Hshow the phase difference function Φ(y) and the slope of Φ(y),respectively, of surface #4 of this embodiment.

EMBODIMENT 7

The collimator lens 1 relating to Embodiment 7 is constructedapproximately the same as Embodiment 5, however, the surface of thelight source side of the second lens element L₂ is an aspherical DOEsurface.

Table 7 below lists the surface number #, in order from the collimatedlight side of the collimator lens, the radius of curvature R (in mm) ofeach lens element surface, the spacing D (in mm) between the surfaces,as well as the refractive index N at the wavelengths 760 nm, 780 nm and800 nm. The surface with a * to the right of the surface number is anaspheric, DOE surface. In the middle portion of the table, are listedthe numerical aperture NA, the focal length f′ of the collimator lens,the focal length f₁ of the first lens element in order from thecollimated light side, and the focal length f₂ of the second lenselement in order from the collimated light side. In the lower portion ofthe table are listed the values of k, a₄, a₆, a₈, and a₁₀, as well asthe values of the coefficients b₁, b₂, and b₃ for Equations (1) and (2)above relating to surface #3 and surface #4.

TABLE 7 # R D N<760 nm> N<780 nm> N<800 nm> 1 −5.330 4.583 1.791751.79092 1.79013 2 −7.504 2.500 3 8.693 4.333 1.58302 1.58252 1.58205 4*−111.888 NA = 0.30 f′ = 10 f₁ = −337.07 f₂ = 13.42 Aspherical and DOEcoefficients of surface #4: k  =  1.0029 b₁ = −1.6069 × 10 a₄  =  3.3910× 10⁻⁴ b₂ =  3.1434 × 10⁻³ a₆  = −1.4141 × 10⁻⁶ b₃ = −2.8091 × 10⁻⁵ a₈ =  5.2720 × 10⁻⁸ a₁₀ = −6.8888 × 10⁻¹⁰

FIGS. 10A-10F show the spherical aberration, astigmatism, distortion,lateral color, phase difference function Φ(y), and slope of Φ(y),respectively, of the collimator lens of Embodiment 7.

EMBODIMENT 8

The collimator lens 1 relating to Embodiment 8 is constructedapproximately the same as in Embodiment 2, however, both surfaces of thesecond lens element L₂ in Embodiment 8 are made to be aspherical DOEsurfaces.

Table 8 below lists the surface number #, in order from the collimatedlight side of the collimator lens, the radius of curvature R (in mm) ofeach lens element surface, the spacing D (in mm) between the surfaces,as well as the refractive index N at the wavelengths 760 nm, 780 nm and800 nm. The surfaces with a * to the right of the surface number areaspheric, DOE surfaces. In the middle portion of the table, are listedthe numerical aperture NA, the focal length f′ of the collimator lens,the focal length f₁ of the first lens element in order from thecollimated light side, and the focal length f₂ of the second lenselement in order from the collimated light side. In the lower portion ofthe table are listed the values of k, a₄, a₆, a₈, and a₁₀, as well asthe values of the coefficients b₁, b₂, and b₃ for Equations (1) and (2)above relating to surfaces #3 and #4.

TABLE 8 # R D N<760 nm> N<780 nm> N<800 nm> 1 −7.310 4.167 1.762791.76202 1.76129 2 −16.105 2.205 3* 10.762 3.833 1.58302 1.58252 1.582054* −10.668 NA = 0.30 f′ = 10 f₁ = −22.09 f₂ = 9.64 Aspherical and DOEAspherical and DOE coefficients of surface #3: coefficients of Surface#4: k  =  1.0303 k  =  9.4924 × 10⁻¹ a₄  = −2.4556 × 10⁻⁴ a₄  =  2.5614× 10⁻⁴ a₆  = −6.4251 × 10⁻⁷ a₆  = −8.5583 × 10⁻⁷ a₈  = −4.8167 × 10⁻⁹a₈  = −6.7217 × 10⁻⁸ a₁₀ = −3.9804 × 10⁻⁹ a₁₀ = −1.7498 × 10⁻⁹ b₁ =−5.5920 × 10 b₁ = −4.5509 × 10 b₂ =  5.9855 × 10⁻³ b₂ =  2.9884 × 10⁻³b₃ =  1.1597 × 10⁻⁵ b₃ =  6.2177 × 10⁻⁶

FIGS. 11A-11D show the spherical aberration, astigmatism, distortion,and lateral color, respectively, of the collimator lens of Embodiment 8.FIGS. 11E & 11F show the phase difference function Φ(y) and the slope ofΦ(y), respectively, of surface #3 of this embodiment, and FIGS. 11G &11H show the phase difference function Φ(y) and the slope of Φ(y),respectively, of surface #4 of this embodiment.

In each of the above embodiments, the aberration diagrams have beencomputed with a glass plate having an index of refraction that equals1.51, and a thickness of 0.417 mm inserted on the light source side ofthe collimator lens. In addition, in the various aberration diagrams, (ois the half-picture angle. In FIGS. 4B, 5B, 6B, 7B, 8B, 9B, 10B, and11B, the astigmatism is shown for the sagittal (S) and tangential (T)planes.

As is clear from these aberration curves, the aberrations are favorablycorrected for each embodiment of the invention. Further, each embodimentsatisfies Condition (1).

The invention being thus described, it will be obvious that the same maybe varied in many ways. For example, the radius of curvature R of eachlens element, and the spacing D between the lens elements may be readilyscaled to obtain a collimator lens of a desired focal length. Suchvariations are not to be regarded as a departure from the spirit andscope of the invention. Rather the scope of the invention shall bedefined as set forth in the following claims and their legalequivalents. All such modifications as would be obvious to one skilledin the art are intended to be included within the scope of the followingclaims.

What is claimed is:
 1. A collimator lens consisting of two lens elementswhich are fixed in position, wherein the surface of the collimator lensnearest the collimated light side is concave, and at least one of thetwo lens elements includes an aspherical surface having diffractionoptical element zones thereon which provide dispersion of opposite signto the dispersion provided by refraction of light by the lens element onwhich said zones are formed.
 2. The collimator lens of claim 1 wherein,in order from the collimated light side of the collimator lens, thefirst lens element has negative refractive power, and the second lenselement has positive refractive power.
 3. The collimator lens of claim 1wherein, in order from the collimated light side of the collimator lens,the first lens element has positive refractive power, and the secondlens element has positive refractive power.
 4. The collimator lens ofclaim 3, wherein the first lens element has stronger refractive powerthan the second lens element.
 5. The collimator lens of claim 1, whereinthe following condition is satisfied: |dΦ(y)/dy|<300 where |dΦ(y)/dy| isthe absolute value of the slope of Φ(y), with Φ(y) being a phasedifference function defined by the equation Φ(y)=b₁y²+b₂y⁴+b₃y⁶ whereΦ(y) is the phase difference function of the DOE surface, y is thedistance from the optical axis, and b₁, b₂, and b₃ are coefficients. 6.The collimator lens of claim 2, wherein the following condition issatisfied: |dΦ(y)/dy|<300 where |dΦ(y)/dy| is the absolute value of theslope of Φ(y), with Φ(y) being a phase difference function defined bythe equation Φ(y)=b₁y²+b₂y⁴+b₃y⁶ where Φ(y) is the phase differencefunction of the DOE surface, y is the distance from the optical axis,and b₁, b₂, and b₃ are coefficients.
 7. The collimator lens of claim 3,wherein the following condition is satisfied:  |dΦ(y)/dy|<300 where|dΦ(y)/dy| is the absolute value of the slope of Φ(y), with Φ(y) being aphase difference function defined by the equation Φ(y)=b₁y²+b₂y⁴+b₃y⁶where Φ(y) is the phase difference function of the DOE surface, y is thedistance from the optical axis, and b₁, b₂, and b₃ are coefficients. 8.The collimator lens of claim 4, wherein the following condition issatisfied: |dΦ(y)/dy|<300 where |dΦ(y)/dy| is the absolute value of theslope of Φ(y), with Φ(y) being a phase difference function defined bythe equation Φ(y)=b₁y²+b₂y⁴+b₃y⁶ where Φ(y) is the phase differencefunction of the DOE surface, y is the distance from the optical axis,and b₁, b₂, and b₃ are coefficients.
 9. The collimator lens of claim 1,in combination with an optical scanning device that includes a rotatingmirror.
 10. The collimator lens of claim 2, in combination with anoptical scanning device that includes a rotating mirror.
 11. Thecollimator lens of claim 3, in combination with an optical scanningdevice that includes a rotating mirror.
 12. The collimator lens of claim4, in combination with an optical scanning device that includes arotating mirror.
 13. The collimator lens of claim 5, in combination withan optical scanning device that includes a rotating mirror.